In a televised news conference, Mr Kan said the country should harness renewable energy sources.
The 11 March earthquake and tsunami wrecked the Fukushima plant, which continues to leak radioactive material.
A large section of public opinion has turned against nuclear power.
About 30% of Japan's electricity was nuclear generated before the Fukushima crisis, and the country had targeted raising that figure to 53% by 2030.
But Mr Kan had already said this commitment should be scrapped.
On Wednesday, he went a step further, saying: "We will aim at realising a society which can exist without nuclear power."
He said the country should aim to develop alternative energy sources such as solar, wind and biomass.
But he did not lay out a timescale for his plan.